How is the graph of y=4 (2)^x+3 translated from the graph of y=4 (2)^x?

Let's log 10 on both side of the equation for both of your equations 

You'll get log y = ( x-3 )log 8 
and log y = x log 8 

Lets assume that a graph of log y against x is plotted.Then log y becomes the y variable, log 8 becomes the gradient and x becomes the x variable. To make visualizing easier, lets assume the gradient is m=log 8= 1. 
So the two log equation becomes, 

y= x 

and 

y= x-3 

Thus, from the x intercept we can see that the graph of y = 4(2)^x-3 is translated from the graph y=4(2)^x 3 units down .